Accelerated degradation analysis based on a random-effect Wiener process with one-order autoregressive errors

• Autorzy: Li Junxing , Wang Zhihua , Liu Chengrui , Qiu Ming

Identyfikatory

DOI

10.17531/ein.2019.2.8

Warianty tytułu

PL

Przyspieszona analiza degradacji w oparciu o proces Wienera z efektem losowym z błędami autoregresyjnymi pierwszego rzędu

• Języki publikacji: EN

Abstrakty

EN

For highly reliable and long-life products, accelerated degradation test (ADT) is often an effective and attractive way to assess the reliability. To analyze the accelerated degradation data, it has been well recognized that it is necessary to incorporate three sources of variability including the temporal variability, the unit-to-unit variability and measurement errors into the ADT model. The temporal variability can be properly described by the Wiener process. However, the randomness of the initial degradation level, which is an important part of the unit-to-unit variability, has been often neglected. In addition, regarding the measurement errors, current ADT models often assumed them to follow a mutually independent normal distribution and ignored the autocorrelation that may probably exist in them. These problems lead to a poor accuracy for reliability evaluation in some situation. Thus, a random-effect Wiener process-based ADT model considering one-order autoregressive (AR(1)) errors is proposed. Then closed-form expressions for the failure time distribution (FTD) is derived based on the concept of first hitting time (FHT). A statistical inference method is adopted to estimate unknown parameters. Finally, a comprehensive simulation study and a practical application are given to demonstrate the rationality and effectiveness of the proposed model.

PL

W przypadku wysoce niezawodnych produktów o długim cyklu życia, przyspieszone badanie degradacji (ADT) często stanowi skuteczny i atrakcyjny sposób oceny niezawodności. Jak wiadomo, analiza danych z przyspieszonej degradacji wymaga włączenia do modelu ADT trzech źródeł zmienności, w tym zmienności czasowej, zmienności między jednostkami i błędów pomiarowych. Zmienność czasową można odpowiednio opisać za pomocą procesu Wienera. Jednak losowość początkowego poziomu degradacji, który stanowi ważną część zmienności między jednostkami, jest często w badaniach pomijana. Ponadto, w odniesieniu do błędów pomiaru, obecne modele ADT często zakładają, że mają one wzajemnie niezależne rozkłady normalne, ignorując możliwą autokorelację. Problemy te prowadzą w niektórych sytuacjach do niskiej trafności oceny niezawodności. W związku z powyższym, zaproponowano model ADT oparty na procesie Wienera z efektem losowym, w którym uwzględniono błędy autoregresyjne pierwszego rzędu (AR (1)). Następnie, w oparciu o pojęcie pierwszego czasu przejścia, wyprowadzono wyrażenia w postaci zamkniętej dla rozkładu czasu uszkodzenia (FTD). Do oszacowania nieznanych parametrów przyjęto metodę wnioskowania statystycznego. Na koniec przedstawiono kompleksowe studium symulacyjne i wskazano praktyczne zastosowanie modelu w celu wykazania jego racjonalności i skuteczności.

Słowa kluczowe

EN

reliability evaluation; accelerated degradation modeling; Wiener process; unit-to-unit variability; measurement errors

PL

ocena niezawodności; przyspieszone modelowanie degradacji; proces Wienera; zmienność między jednostkami; błędy pomiaru

• Wydawca: Polskie Naukowo-Techniczne Towarzystwo Eksploatacyjne
• Czasopismo: Eksploatacja i Niezawodność
• Rocznik: 2019
• Tom: Vol. 21, no. 2
• Strony: 246--255
• Opis fizyczny: Bibliogr. 35 poz., rys., tab.

Twórcy

autor

Li Junxing

• School of Mechatronical Engineering Henan University of Science and Technology Luoyang 471003, China

autor

Wang Zhihua

• School of Aeronautic Science and Engineering Beihang University Beijing 100191, China

autor

Liu Chengrui

• Beijing Institute of Control Engineering Beijing 100080, China

autor

Qiu Ming

• School of Mechatronical Engineering Henan University of Science and Technology Luoyang 471003, China

Bibliografia

• 1. Chen D G, Lio Y, Ng H K T, Tsai T R. Statistical Modeling for Degradation Data. Springer, 2017, https://doi.org/10.1007/978-981-10-5194-4.
• 2. Chhikara R S, Folks J L. The inverse Gaussian distribution: theory, methodology, and applications, Marcel Dekker, Inc.1989.
• 3. Chi E M, Reinsel G C. Models for longitudinal data with random effects and AR (1) errors, Publications of the American Statistical Association 1989; 84: 452-459, https://doi.org/10.1080/01621459.1989.10478790.
• 4. Hao S, Yang J, Berenguer C. Nonlinear step-stress accelerated degradation modelling considering three sources of variability, Reliability Engineering & System Safety 2017; 172.
• 5. Josephlu C, Meeker W. Using degradation measures to estimate a Time-to-Failure distribution. Technometrics 1993: 161-174.
• 6. Lei Y, Li N, Jia F, Lin J, Xing S. A nonlinear degradation model based method for remaining useful life prediction of rolling element bearings, Prognostics and System Health Management Conference 2016: 1-8.
• 7. Li J, Wang Z, Liu X, Zhang Y, Fu H, Liu C. A Wiener process model for accelerated degradation analysis considering measurement errors, Microelectronics Reliability 2016; 65: 8-15,https://doi.org/10.1016/j.microrel.2016.08.004.
• 8. Li J, Wang Z, Zhang Y, Fu H, Liu C, Krishnaswamy S. Degradation data analysis based on a generalized Wiener process subject to measurement error, Mechanical Systems & Signal Processing 2017; 94: 57-72, https://doi.org/10.1016/j.ymssp 2017.02.031.
• 9. Li J, Wang Z, Zhang Y, Liu C, Fu H. A nonlinear Wiener process degradation model with autoregressive errors, Reliability Engineering & System Safety 2018: 173, https://doi.org/10.1016/j.ress.2017.11.003.
• 10. Liao C M, Tseng S T. Optimal design for step-stress accelerated degradation tests, IEEE Transactions on Reliability 2006; 55(1):59-66, https://doi.org/10.1109/TR.2005.863811.
• 11. Lim H, Yum B J. Optimal design of accelerated degradation tests based on Wiener process models, Journal of Applied Statistics 2011; 38(2):17-27, https://doi.org/10.1080/02664760903406488.
• 12. Limon S, Yadav O P, Liao H. A literature review on planning and analysis of accelerated testing for reliability assessment. Quality and Reliability Engineering International 2017; 33: 2361-2383, https://doi.org/10.1002/qre.2195.
• 13. Lin J, Wei B. Testing for heteroscedasticity and/or autocorrelation in longitudinal mixed effect nonlinear models with AR(1) errors. Commun Stat –Theory Methods 2007; 36: 67–86, https://doi.org/10.1080/03610920601001816.
• 14. Liu L, Li X, Sun F, Wang N. A General Accelerated Degradation Model Based on the Wiener Process, Materials 2016; 9, https://doi.org/10.3390/ma9120981.
• 15. Lu J. Degradation processes and related reliability models, Ph.D. thesis. Montreal, Canada: McGill University,1995.
• 16. Lu C J, Meeker W Q, Escobar L A. A comparison of degradation and failure-time analysis methods for estimating a time-to-failure distribution. Stat. Sin. 1996; 6: 531–546.
• 17. Madsen H, Time Series Analysis, Chapman & Hall/crc Boca Raton, 2007.
• 18. Meeker W Q, Escobar L A. Statistical methods for reliability data, John Wiley & Sons, 2014.
• 19. Pan D, Wei Y, Fang H, Yang W. A reliability estimation approach via Wiener degradation model with measurement errors. Applied Mathematics & Computation, 2018; 320,https://doi.org/10.1016/j.amc.2017.09.020.
• 20. Peng C Y, Tseng S T. Mis-Specification Analysis of Linear Degradation Models, IEEE Transactions on Reliability 2009; 58: 444-455, https://doi.org/10.1109/TR.2009.2026784.
• 21. Shahraki A F, Yadav O P, Liao H. A Review on Degradation Modelling and Its Engineering Applications, International Journal of Performability Engineering 2017;13: 299-314, https://doi.org/10.23940/ijpe.17.03.p6.299314.
• 22. Si X S, Wang W, Hu C H, Chen M Y, Zhou D H. A Wiener-process-based degradation model with a recursive filter algorithm for remaining useful life estimation, Mechanical Systems & Signal Processing 2013; 35: 219-237, https://doi.org/10.1016/j.ymssp.2012.08.016.
• 23. Si X S, Wang W, Hu C H, Zhou D H. Estimating remaining useful life with three-source variability in degradation modeling. IEEE Transactions on Reliability 2014; 63:167-190, https://doi.org/10.1109/TR.2014.2299151.
• 24. Sun L, Gu X, Song P. Accelerated Degradation Process Analysis Based on the Nonlinear Wiener Process with Covariates and Random Effects, Mathematical Problems in Engineering 2016; 1-13, https://doi.org/10.1155/2016/5246108.
• 25. Tang S, Guo X, Yu C, Xue H, Zhou Z. Accelerated Degradation Tests Modeling Based on the Nonlinear Wiener Process with Random Effects, Mathematical Problems in Engineering 2014: 1-11,https://doi.org/10.1155/2014/560726.
• 26. Vališ D, Žák L, Pokora O. Perspective approach in using anti-oxidation and anti-wear particles from oil to estimate residual technical life of a system, Tribology International 2018; 118: 46-59, https://doi.org/10.1016/j.triboint.2017.09.017.
• 27. Vališ D, Žák L, Pokora O, Lánský P. Perspective analysis outcomes of selected tribodiagnostic data used as input for condition based maintenance, Reliability Engineering & System Safety 2016; 145: 231-242,https://doi.org/10.1016/j.ress.2015.07.026.
• 28. Vališ D, Nováček O, Hasilová K, Leuchter J. Modelling of degradation and a soft failure moment during the operation of a supercapacitor applying selected diffusion processes, Engineering Failure Analysis 2017; 82: 566-582, https://doi.org/10.1016/j.engfailanal.2017.04.019.
• 29. Whitmore G A. Estimating degradation by a wiener diffusion process subject to measurement error, Lifetime Data Analysis 1995; 1: 307-319, https://doi.org/10.1007/BF00985762.
• 30. Whitmore G A, Schenkelberg F. Modelling accelerated degradation data using Wiener diffusion with a time scale transformation, Lifetime Data Analysis 1997; 3: 27-45, https://doi.org/10.1023/A:1009664101413.
• 31. Yang G. Life cycle reliability engineering. Wiley, 2008.
• 32. Ye Z S, Wang Y, Tsui K L, Pecht M. Degradation Data Analysis Using Wiener Processes With Measurement Errors, IEEE Transactions on Reliability 2013; 62: 772-780, https://doi.org/10.1109/TR.2013.2284733.
• 33. Ye Z S, Xie M. Stochastic modelling and analysis of degradation for highly reliable products, Applied Stochastic Models in Business & Industry 2015; 31: 16-32, https://doi.org/10.1002/asmb.2063.
• 34. Zhang Z, Si X, Hu C, Lei Y. Degradation Data Analysis and Remaining Useful Life Estimation: A Review on Wiener-Process-Based Methods, European Journal of Operational Research 2018,https://doi.org/10.1016/j.ejor.2018.02.033.
• 35. Zheng J F, Si X S, Hu C H, Zhang Z X, Jiang W. A Nonlinear Prognostic Model for Degrading Systems With Three-Source Variability, IEEE Transactions on Reliability 2016; 65: 736-750, https://doi.org/10.1109/TR.2015.2513044.